Optimizing Robust Quantum Gates in Open Quantum Systems

We are currently at the cusp of a revolution in quantum technology that relies not just on the passive use of quantum effects, but on their active control. At the forefront of this revolution is the implementation of a quantum computer. Encoding information in quantum states as “qubits” allows to use entanglement and quantum superposition to perform calculations that are infeasible on classical computers. The fundamental challenge in the realization of quantum computers is to avoid decoherence – the loss of quantum properties – due to unwanted interaction with the environment. This thesis addresses the problem of implementing entangling two-qubit quantum gates that are robust with respect to both decoherence and classical noise. It covers three aspects: the use of efficient numerical tools for the simulation and optimal control of open and closed quantum systems, the role of advanced optimization functionals in facilitating robustness, and the application of these techniques to two of the leading implementations of quantum computation, trapped atoms and superconducting circuits. After a review of the theoretical and numerical foundations, the central part of the thesis starts with the idea of using ensemble optimization to achieve robustness with respect to both classical fluctuations in the system parameters, and decoherence. For the example of a controlled phasegate implemented with trapped Rydberg atoms, this approach is demonstrated to yield a gate that is at least one order of magnitude more robust than the best known analytic scheme. Moreover this robustness is maintained even for gate durations significantly shorter than those obtained in the analytic scheme. Superconducting circuits are a particularly promising architecture for the implementation of a quantum computer. Their flexibility is demonstrated by performing optimizations for both diagonal and non-diagonal quantum gates. In order to achieve robustness with respect to decoherence, it is essential to implement quantum gates in the shortest possible amount of time. This may be facilitated by using an optimization functional that targets an arbitrary perfect entangler, based on a geometric theory of two-qubit gates. For the example of superconducting qubits, it is shown that this approach leads to significantly shorter gate durations, higher fidelities, and faster convergence than the optimization towards specific two-qubit gates. Performing optimization in Liouville space in order to properly take into account decoherence poses significant numerical challenges, as the dimension scales quadratically compared to Hilbert space. However, it can be shown that for a unitary target, the optimization only requires propagation of at most three states, instead of a full basis of Liouville space. Both for the example of trapped Rydberg atoms, and for superconducting qubits, the successful optimization of quantum gates is demonstrated, at a significantly reduced numerical cost than was previously thought possible. Together, the results of this thesis point towards a comprehensive framework for the optimization of robust quantum gates, paving the way for the future realization of quantum computers.

Excitation of Phonons in Solids and Nanostructures by Intense Laser and XUV Pulses and by Low Energy Atomic Collision

Intensive, ultrakurze Laserpulse regen Festkörper in einen Zustand an, in dem die Elektronen hohe Temperaturen erlangen, während das Gitter kalt bleibt. Die heißen Elektronen beeinflussen das sog. Laser-angeregte interatomare Potential bzw. die Potentialenergiefläche, auf der die Ionen sich bewegen. Dieses kann neben anderen ultrakurzen Prozessen zu Änderungen der Phononfrequenzen (phonon softening oder phonon hardening) führen. Viele ultrakurze strukturelle Phänomene in Festkörpern hängen bei hohen Laseranregungen von Änderungen der Phononfrequenzen bei niedrigeren Anregungen ab. Um die Laser-bedingten Änderungen des Phononenspektrums von Festkörpern beschreiben zu können, haben wir ein auf Temperatur-abhängiger Dichtefunktionaltheorie basierendes Verfahren entwickelt. Die dramatischen Änderungen nach einer Laseranregung in der Potentialenergiefläche werden durch die starke Veränderung der Zustandsdichte und der Besetzungen der Elektronen hervorgerufen. Diese Änderungen in der Zustandsdichte und den Besetzungszahlen können wir mit unserer Methode berechnen, um dann damit das Verhalten der Phononen nach einer Laseranregung zu analysieren. Auf diese Art und Weise studierten wir den Einfluss einer Anregung mit einem intensiven, ultrakurzen Laserpuls auf repräsentative Phonon Eigenmoden in Magnesium, Kupfer und Aluminium. Wir stellten dabei in manchen Gitterschwingungen entweder eine Abnahme (softening) und in anderen eine Zunahme (hardening) der Eigenfrequenz fest. Manche Moden zeigten bei Variation der Laseranregungsstärke sogar beide Verhaltensweisen. Das eine Phonon-Eigenmode ein hardening und softening zeigen kann, wird durch das Vorhandensein von van Hove Singularitäten in der elektronischen Zustandsdichte des betrachteten Materials erklärt. Für diesen Fall stellt unser Verfahren zusammen mit der Sommerfeld-Entwicklung die Eigenschaften der Festkörper Vibrationen in Verbindung mit den Laser induzierten Veränderungen in den elektronischen Besetzungen für verschiedene Phonon-eingefrorene Atomkonfigurationen. Auch die absolute Größe des softening und hardening wurde berechnet. Wir nehmen an, dass unsere Theorie Licht in die Effekte der Laseranregung von verschiedenen Materialien bringt. Außerdem studierten wir mit Hilfe von Dichtefunktionaltheorie die strukturellen Material-Eigenschaften, die durch kurze XUV Pulse induziert werden. Warme dichte Materie in Ultrakurzpuls angeregten Magnesium wurde analysiert und verglichen mit den Ergebnissen bei durch Laser Anregung bedingten Änderungen. Unter Verwendung von elektronischer-Temperatur-abhängiger Dichtefunktionaltheorie wurden die Änderungen in den Bindungseigenschaften von warmen dichten Magnesium studiert. Wir stellten dabei beide Effekte, Verstärkung und Abschwächung von Bindungen, bei jeweils verschiedenen Phonon Eigenmoden von Magnesium auf Grund von der Erzeugung von Rumpflöchern und dem Vorhandensein von heißen Elektronen fest. Die zusätzliche Erzeugung von heißen Elektronen führt zu einer Änderung der Bindungscharakteristik, die der Änderung, die durch die bereits vorhandenen Rumpflöcher hervorgerufen wurde, entgegen wirkt. Die thermischen Eigenschaften von Nanostrukturen sind teilweise sehr wichtig für elektronische Bauteile. Wir studierten hier ebenfalls den Effekt einer einzelnen Graphen Lage auf Kupfer. Dazu untersuchten wir mit Dichtefunktionaltheorie die strukturellen- und Schwingungseigenschaften von Graphen auf einem Kupfer Substrat. Wir zeigen, dass die schwache Wechselwirkung zwischen Graphen und Kupfer die Frequenz der aus der Ebene gerichteten akustischen Phonon Eigenmode anhebt und die Entartung zwischen den aus der Ebene gerichteten akustischen und optischen Phononen im K-Punkt des Graphen Spektrums aufhebt. Zusätzlich führten wir ab initio Berechnungen zur inelastischen Streuung eines Helium Atoms mit Graphen auf einem Kuper(111) Substrat durch. Wir berechneten dazu das Leistungsspektrum, das uns eine Idee über die verschiedenen Gitterschwingungen des Graphene-Kuper(111) Systems gibt, die durch die Kollision des Helium Atom angeregt werden. Wir brachten die Positionen der Peaks im Leistungsspektrum mit den Phonon Eigenfrequenzen, die wir aus den statischen Rechnungen erhalten haben, in Beziehung. Unsere Ergebnisse werden auch verglichen mit den Ergebnissen experimenteller Daten zur Helium Streuung an Graphen-Kupfer(111) Oberflächen.

ACTORS: A Model of Concurrent Computation in Distributed Systems

A foundational model of concurrency is developed in this thesis. We examine issues in the design of parallel systems and show why the actor model is suitable for exploiting large-scale parallelism. Concurrency in actors is constrained only by the availability of hardware resources and by the logical dependence inherent in the computation. Unlike dataflow and functional programming, however, actors are dynamically reconfigurable and can model shared resources with changing local state. Concurrency is spawned in actors using asynchronous message-passing, pipelining, and the dynamic creation of actors. This thesis deals with some central issues in distributed computing. Specifically, problems of divergence and deadlock are addressed. For example, actors permit dynamic deadlock detection and removal. The problem of divergence is contained because independent transactions can execute concurrently and potentially infinite processes are nevertheless available for interaction.

A Distributed Model for Mobile Robot Environment-Learning and Navigation

A distributed method for mobile robot navigation, spatial learning, and path planning is presented. It is implemented on a sonar-based physical robot, Toto, consisting of three competence layers: 1) Low-level navigation: a collection of reflex-like rules resulting in emergent boundary-tracing. 2) Landmark detection: dynamically extracts landmarks from the robot's motion. 3) Map learning: constructs a distributed map of landmarks. The parallel implementation allows for localization in constant time. Spreading of activation computes both topological and physical shortest paths in linear time. The main issues addressed are: distributed, procedural, and qualitative representation and computation, emergent behaviors, dynamic landmarks, minimized communication.

Analysis and Implementation of Robust Grasping Behaviors

This thesis addresses the problem of developing automatic grasping capabilities for robotic hands. Using a 2-jointed and a 4-jointed nmodel of the hand, we establish the geometric conditions necessary for achieving form closure grasps of cylindrical objects. We then define and show how to construct the grasping pre-image for quasi-static (friction dominated) and zero-G (inertia dominated) motions for sensorless and sensor-driven grasps with and without arm motions. While the approach does not rely on detailed modeling, it is computationally inexpensive, reliable, and easy to implement. Example behaviors were successfully implemented on the Salisbury hand and on a planar 2-fingered, 4 degree-of-freedom hand.

Heterogeneous Multi-Robot Cooperation

This report addresses the problem of achieving cooperation within small- to medium- sized teams of heterogeneous mobile robots. I describe a software architecture I have developed, called ALLIANCE, that facilitates robust, fault tolerant, reliable, and adaptive cooperative control. In addition, an extended version of ALLIANCE, called L-ALLIANCE, is described, which incorporates a dynamic parameter update mechanism that allows teams of mobile robots to improve the efficiency of their mission performance through learning. A number of experimental results of implementing these architectures on both physical and simulated mobile robot teams are described. In addition, this report presents the results of studies of a number of issues in mobile robot cooperation, including fault tolerant cooperative control, adaptive action selection, distributed control, robot awareness of team member actions, improving efficiency through learning, inter-robot communication, action recognition, and local versus global control.

Implementing Distributed Systems Using Linear Naming

Linear graph reduction is a simple computational model in which the cost of naming things is explicitly represented. The key idea is the notion of "linearity". A name is linear if it is only used once, so with linear naming you cannot create more than one outstanding reference to an entity. As a result, linear naming is cheap to support and easy to reason about. Programs can be translated into the linear graph reduction model such that linear names in the program are implemented directly as linear names in the model. Nonlinear names are supported by constructing them out of linear names. The translation thus exposes those places where the program uses names in expensive, nonlinear ways. Two applications demonstrate the utility of using linear graph reduction: First, in the area of distributed computing, linear naming makes it easy to support cheap cross-network references and highly portable data structures, Linear naming also facilitates demand driven migration of tasks and data around the network without requiring explicit guidance from the programmer. Second, linear graph reduction reveals a new characterization of the phenomenon of state. Systems in which state appears are those which depend on certain -global- system properties. State is not a localizable phenomenon, which suggests that our usual object oriented metaphor for state is flawed.

Safe Distributed Coordination of Heterogeneous Robots through Dynamic Simple Temporal Networks

Research on autonomous intelligent systems has focused on how robots can robustly carry out missions in uncertain and harsh environments with very little or no human intervention. Robotic execution languages such as RAPs, ESL, and TDL improve robustness by managing functionally redundant procedures for achieving goals. The model-based programming approach extends this by guaranteeing correctness of execution through pre-planning of non-deterministic timed threads of activities. Executing model-based programs effectively on distributed autonomous platforms requires distributing this pre-planning process. This thesis presents a distributed planner for modelbased programs whose planning and execution is distributed among agents with widely varying levels of processor power and memory resources. We make two key contributions. First, we reformulate a model-based program, which describes cooperative activities, into a hierarchical dynamic simple temporal network. This enables efficient distributed coordination of robots and supports deployment on heterogeneous robots. Second, we introduce a distributed temporal planner, called DTP, which solves hierarchical dynamic simple temporal networks with the assistance of the distributed Bellman-Ford shortest path algorithm. The implementation of DTP has been demonstrated successfully on a wide range of randomly generated examples and on a pursuer-evader challenge problem in simulation.

Generative Temporal Planning with Complex Processes

Autonomous vehicles are increasingly being used in mission-critical applications, and robust methods are needed for controlling these inherently unreliable and complex systems. This thesis advocates the use of model-based programming, which allows mission designers to program autonomous missions at the level of a coach or wing commander. To support such a system, this thesis presents the Spock generative planner. To generate plans, Spock must be able to piece together vehicle commands and team tactics that have a complex behavior represented by concurrent processes. This is in contrast to traditional planners, whose operators represent simple atomic or durative actions. Spock represents operators using the RMPL language, which describes behaviors using parallel and sequential compositions of state and activity episodes. RMPL is useful for controlling mobile autonomous missions because it allows mission designers to quickly encode expressive activity models using object-oriented design methods and an intuitive set of activity combinators. Spock also is significant in that it uniformly represents operators and plan-space processes in terms of Temporal Plan Networks, which support temporal flexibility for robust plan execution. Finally, Spock is implemented as a forward progression optimal planner that walks monotonically forward through plan processes, closing any open conditions and resolving any conflicts. This thesis describes the Spock algorithm in detail, along with example problems and test results.

Fast Sorting on a Distributed-Memory Architecture

We consider the often-studied problem of sorting, for a parallel computer. Given an input array distributed evenly over p processors, the task is to compute the sorted output array, also distributed over the p processors. Many existing algorithms take the approach of approximately load-balancing the output, leaving each processor with Θ(n/p) elements. However, in many cases, approximate load-balancing leads to inefficiencies in both the sorting itself and in further uses of the data after sorting. We provide a deterministic parallel sorting algorithm that uses parallel selection to produce any output distribution exactly, particularly one that is perfectly load-balanced. Furthermore, when using a comparison sort, this algorithm is 1-optimal in both computation and communication. We provide an empirical study that illustrates the efficiency of exact data splitting, and shows an improvement over two sample sort algorithms.

Scaling algorithms for distributed max flow

Bibliography: p. 22-24.

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr) transformation to obtain the random vector y of dimension D. The factor model is then y = Λf + e (1) with the factors f of dimension k < D, the error term e, and the loadings matrix Λ. Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysis model (1) can be written as Cov(y) = ΛΛT + ψ (2) where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as the loadings matrix Λ are estimated from an estimation of Cov(y). Given observed clr transformed data Y as realizations of the random vector y. Outliers or deviations from the idealized model assumptions of factor analysis can severely effect the parameter estimation. As a way out, robust estimation of the covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), see Pison et al. (2003). Well known robust covariance estimators with good statistical properties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), rely on a full-rank data matrix Y which is not the case for clr transformed data (see, e.g., Aitchison, 1986). The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves this singularity problem. The data matrix Y is transformed to a matrix Z by using an orthonormal basis of lower dimension. Using the ilr transformed data, a robust covariance matrix C(Z) can be estimated. The result can be back-transformed to the clr space by C(Y ) = V C(Z)V T where the matrix V with orthonormal columns comes from the relation between the clr and the ilr transformation. Now the parameters in the model (2) can be estimated (Basilevsky, 1994) and the results have a direct interpretation since the links to the original variables are still preserved. The above procedure will be applied to data from geochemistry. Our special interest is on comparing the results with those of Reimann et al. (2002) for the Kola project data

Robust fault detection using consistency techniques for uncertainty handling

Often practical performance of analytical redundancy for fault detection and diagnosis is decreased by uncertainties prevailing not only in the system model, but also in the measurements. In this paper, the problem of fault detection is stated as a constraint satisfaction problem over continuous domains with a big number of variables and constraints. This problem can be solved using modal interval analysis and consistency techniques. Consistency techniques are then shown to be particularly efficient to check the consistency of the analytical redundancy relations (ARRs), dealing with uncertain measurements and parameters. Through the work presented in this paper, it can be observed that consistency techniques can be used to increase the performance of a robust fault detection tool, which is based on interval arithmetic. The proposed method is illustrated using a nonlinear dynamic model of a hydraulic system

Automatic self-configuration of the logical network using distributed software agents

We present a system for dynamic network resource configuration in environments with bandwidth reservation. The proposed system is completely distributed and automates the mechanisms for adapting the logical network to the offered load. The system is able to manage dynamically a logical network such as a virtual path network in ATM or a label switched path network in MPLS or GMPLS. The system design and implementation is based on a multi-agent system (MAS) which make the decisions of when and how to change a logical path. Despite the lack of a centralised global network view, results show that MAS manages the network resources effectively, reducing the connection blocking probability and, therefore, achieving better utilisation of network resources. We also include details of its architecture and implementation